A diesel engine in which an engine exhaust passage is branched to a pair of exhaust branch passages for purifying NO.sub.x in the diesel engine, a switching valve is disposed at the branched portion of these exhaust branch passages, the switching valve is switched each time a predetermined time passes to alternately guide the exhaust gas to one of the exhaust branch passages, and a catalyst which can oxidize and absorb the NO.sub.x is disposed in each of the exhaust branch passages is well known (refer to Japanese Unexamined Patent Publication No. 62-106826). In this diesel engine, the NO.sub.x in the exhaust gas introduced into one exhaust branch passage is oxidized and absorbed by the catalyst disposed in that exhaust branch passage. During this time, the inflow of the exhaust gas to the other exhaust branch passage is stopped and, at the same time, a gaseous reducing agent is fed into this exhaust branch passage. The NO.sub.x accumulated in the catalyst disposed in this exhaust branch passage is reduced by this reducing agent. Subsequently, after the elapse of a predetermined time, the introduction of the exhaust gas to the exhaust branch passage to which the exhaust gas had been introduced heretofore is stopped by the switching function of the switching valve, and the introduction of the exhaust gas to the exhaust branch passage to which the introduction of the exhaust gas had been stopped heretofore is started again. That is, in this diesel engine, seen from the viewpoint of each of the exhaust branch passages, exhaust gas is made to flow for a predetermined time during which the NO.sub.x in the exhaust gas is oxidized and absorbed by the catalyst, then the inflow of exhaust gas is stopped for a predetermined period and a reducing agent is fed, whereby the NO.sub.x accumulated in the catalyst is reduced.
However, in this diesel engine, when the NO.sub.x was to be reduced, there was the problem that the inflow of the exhaust gas to the catalyst was stopped, but that the NO.sub.x was attempted to be reduced while causing exhaust gas to flow into the catalyst. That is, with such a catalyst, the speed of reduction of the NO.sub.x changed depending on the temperature of the catalyst and as the temperature of the catalyst became lower, the speed of reduction of the NO.sub.x became slower. Accordingly, where the temperature of the catalyst is low, if a reducing agent is fed for a predetermined period, when the period of feeding the reducing agent is short, the NO.sub.x absorbed in the catalyst cannot be sufficiently reduced, so a large amount of NO.sub.x remains in the catalyst and therefore the NO.sub.x absorption capacity ends up being reduced. As a result, there was the problem that the NO.sub.x absorption capacity becomes saturated in a short time after the feeding of the reducing agent is stopped and the NO.sub.x absorption action started and therefore the NO.sub. x is released into the atmosphere.
Further, if a large amount of the reducing agent is fed when the temperature of the catalyst is low, only a small amount of the reducing agent is used for the reduction of the NO.sub.x due to the slow speed of reduction of the NO.sub.x, therefore there was the problem that a large amount of the reducing agent is released in the atmosphere. On the other hand, if the amount of the reducing agent is reduced to solve this problem, then even when the temperature of the catalyst is high and therefore the speed of reduction of NO.sub.x is fast, only part of the NO.sub.x is reduced and therefore a large amount of NO.sub.x remains in the catalyst, so the NO.sub.x absorption capacity ends up reduced. As a result, there is the problem that the NO.sub.x absorption capacity ends up saturated in a short time after the feeding of the reducing agent is stopped and the NO.sub.x absorption action is started and therefore the NO.sub.x is released into the atmosphere.